To start with, we discuss in Sec.  a model
that involves a time-dependent noise intensity (diffusivity). A
prominent example of such a process (which was originally proposed by
Batchelor in the context of turbulence [1]}) is scaled
Brownian motion [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}. In the present paper, we utilize this rather simple, and
still Markovian, generalization of standard Brownian motion to review
some core concepts of ST definitions. In particular, we discuss the
role of the FDR and, related to that, the definition of an (effective)
temperature
[11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}
for definitions of heat production and the validity of the standard
IFR for the entropy production.
